Let's break down the problem step by step.
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Equation: We need to write an equation based on the statement: "A number decreased by sixty-eight is thirty-one." If we let the variable \( x \) represent the unknown number, the equation would be: \[ x - 68 = 31 \]
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This is a: The problem is a subtraction problem, since it involves decreasing a number (subtracting).
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To solve the equation, we need to add 68 to both sides of the equation. The adjustment will isolate \( x \): \[ x - 68 + 68 = 31 + 68 \] \[ x = 99 \]
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To check the solution, we need to substitute 99 for the variable in the equation. We can verify by plugging the value back into the original equation: \[ 99 - 68 = 31 \] Simplifying it gives: \[ 31 = 31 \] This confirms that our solution is correct.
Now let's fill in the blanks:
- Equation: x - 68 = 31
- This is a subtraction problem.
- To solve the equation, add 68 to both sides of the equation.
- To check the solution, substitute 99 for the variable in the equation.